On Trapped Modes of Rotating Fluids in Spherical Shells

The question of existence of axisymmetric, equatorially trapped modes in rotating spherical shells (Stern, 1963; Stewartson and Rickard, 1969) is approached by means of a numerical simulation. The existence of one trapped mode is confirmed, and the dependence of its frequency on the thickness of the shell is investigated. The ray theoretical approach of Bretherton (1964) is also reconsidered, and it is found that in a shell of given thickness there are only a limited number of closed ray patterns which are confined to the vicinity of the equator. A continuous band of frequencies is associated with each one of these rays. It is found that the frequencies derived by the numerical simulation for thin shells agree with the maximum frequency in the first of these bands. It is conjectured that this fact may be associated with the viscous boundary conditions driving the forced oscillations inside the shell.